International Association
for Cryptologic Research

Keccak is widely used in lattice-based cryptography (LBC) and its impact to the overall running time in LBC scheme can be predominant on platforms lacking dedicated SHA-3 instructions. This holds true on embedded devices for Kyber and Dilithium, two LBC schemes selected by NIST to be standardized as quantumsafe cryptographic algorithms. While extensive work has been done to optimize the polynomial arithmetic in these schemes, it was generally assumed that Keccak implementations were already optimal and left little room for enhancement.In this paper, we revisit various optimization techniques for both Keccak and Dilithium on two ARMv7-M processors, i.e., Cortex-M3 and M4. For Keccak, we improve its efficiency using two architecture-specific optimizations, namely lazy rotation and memory access pipelining, on ARMv7-M processors. These optimizations yield performance gains of up to 24.78% and 21.4% for the largest Keccak permutation instance on Cortex-M3 and M4, respectively. As for Dilithium, we first apply the multi-moduli NTT for the small polynomial multiplication cti on Cortex-M3. Then, we thoroughly integrate the efficient Plantard arithmetic to the 16-bit NTTs for computing the small polynomial multiplications csi and cti on Cortex-M3 and M4. We show that the multi-moduli NTT combined with the efficient Plantard arithmetic could obtain significant speed-ups for the small polynomial multiplications of Dilithium on Cortex-M3. Combining all the aforementioned optimizations for both Keccak and Dilithium, we obtain 15.44% ∼ 23.75% and 13.94% ∼ 15.52% speed-ups for Dilithium on Cortex-M3 and M4, respectively. Furthermore, we also demonstrate that the Keccak optimizations yield 13.35% to 15.00% speed-ups for Kyber, and our Keccak optimizations decrease the proportion of time spent on hashing in Dilithium and Kyber by 2.46% ∼ 5.03% on Cortex-M4.

The GIFT family of lightweight block ciphers, published at CHES 2017, offers excellent hardware performance figures and has been used, in full or in part, in several candidates of the ongoing NIST lightweight cryptography competition. However, implementation of GIFT in software seems complex and not efficient due to the bit permutation composing its linear layer (a feature shared with PRESENT cipher). In this article, we exhibit a new non-trivial representation of the GIFT family of block ciphers over several rounds. This new representation, that we call fixslicing, allows extremely efficient software bitsliced implementations of GIFT, using only a few rotations, surprisingly placing GIFT as a very efficient candidate on micro-controllers. Our constant time implementations show that, on ARM Cortex-M3, 128-bit data can be ciphered with only about 800 cycles for GIFT-64 and about 1300 cycles for GIFT-128 (assuming pre-computed round keys). In particular, this is much faster than the impressive PRESENT implementation published at CHES 2017 that requires 2116 cycles in the same setting, or the current best AES constant time implementation reported that requires 1617 cycles. This work impacts GIFT, but also improves software implementations of all other cryptographic primitives directly based on it or strongly related to it.

The fixslicing implementation strategy was originally introduced as a new representation for the hardware-oriented GIFT block cipher to achieve very efficient software constant-time implementations. In this article, we show that the fundamental idea underlying the fixslicing technique is not of interest only for GIFT, but can be applied to other ciphers as well. Especially, we study the benefits of fixslicing in the case of AES and show that it allows to reduce by 52% the amount of operations required by the linear layer when compared to the current fastest bitsliced implementation on 32-bit platforms. Overall, we report that fixsliced AES-128 allows to reach 80 and 91 cycles per byte on ARM Cortex-M and E31 RISC-V processors respectively (assuming pre-computed round keys), improving the previous records on those platforms by 21% and 26%. In order to highlight that our work also directly improves masked implementations that rely on bitslicing, we report implementation results when integrating first-order masking that outperform by 12% the fastest results reported in the literature on ARM Cortex-M4. Finally, we demonstrate the genericity of the fixslicing technique for AES-like designs by applying it to the Skinny-128 tweakable block ciphers.